Yang, Y.; Liu, X., and Zhang, M., 2015. Instability of laminar flow in a wide shallow meander channel.
The meander river has one of the most common types of natural river morphology, where the flow pattern influences the transformation and development of river morphology. The theory of the instability analysis of laminar flow in a wide-shallow meander channel with constant curvature is investigated in this study. The modified Orr-Summerfield equation, which is established in a curvilinear orthogonal coordinate for two-dimensional incompressible flow, is simplified for the case of wide-shallow channel. The characteristics of instability, such as the neutral curve of critical Reynolds number, contour of growth rate and characteristic spectrum of wave number are obtained by performing the numerical simulations. The computed results show that the characteristic spectrum of meander channel is similar to that of straight channel. It can thus be inferred that the flows in both channels have the same stability characteristics. Furthermore, the neutral curve moves leftward and the critical Reynolds number decreases with the increase of bank curvature. Secondly, the response to the disturbance wave number also increases, which results in the instability of the flow. Thus, this study explains the reasons for the laminar flow becoming unstable in meander channel and also establishes the fundamental theory to further study meandering rivers.